Systems and methods for signal processing using power spectral density shape

ABSTRACT

A signal processing method is provided. The signal processing method includes receiving, at a signal processing system, a signal of interest, calculating, using the signal processing system, a power spectral density for the signal of interest, calculating, using the signal processing system, a basis vector based on the power spectral density shape, performing, using the signal processing system, a linear regression using the basis vector to generate an estimate for at least one parameter of the signal of interest, and transmitting, based on the at least one generated estimate, a signal that avoids interference with the signal of interest.

BACKGROUND

The field of the disclosure relates generally to signal processing, and,more particularly, to estimating signal parameters based on powerspectral density shape.

Wireless communication systems that compete for spectrum usage (such asthose operating in white spaces or cognitive radio systems) mustdetermine the presence of existing signals in order to avoid interferingwith those existing signals. This determination may be difficult, andinvolves issues such as the near-far problem. Specifically, while afirst signal from an existing transmitter may be far away or weakrelative to an additional signal source, a receiver may be much closerto the additional signal source. If the additional signal source sendsout a powerful signal in a frequency near a frequency of the firstsignal, the powerful signal may significantly interfere with thereceiver's ability to detect the first signal. This problem isexacerbated further when the first signal is so weak that it isundetectable as an existing signal and simply looks like noise, whichcould lead to transmission directly on top of the first signal.

With exponential growth in wireless communications, both for civilianand military usage, comes the need to cost effectively and quicklymodify a radio device to meet new uses and operate on existingfrequencies. The ideal device would be a single physical radio thatimplements all existing communication signals and protocols, as well asone that adapts to new and future conditions to effectively usedifferent communications resources when desired. Software-defined radio(SDR) technology brings these benefits of flexibility and costefficiency to end users. In order for SDR to participate with othersystems (both SDR and legacy), it must compete for spectrum andcooperate with other systems. In order to cooperate, SDR must be able tosense when other signals are present and avoid interfering with them.

The near-far problem, discussed briefly above, is a problem that existswith current wireless radio networks, including those usingdirect-sequence spread-spectrum multiple access (DS/SSMA) communicationsystems, and also systems that must simply determine which legacy (i.e.,non-spread) signals are present before deciding on a transmit channeland signal type. For example, code division multiple access (CDMA) typesystems achieve multiple-access capability by assigning a distinctsignature waveform to each user from a set of waveforms with low mutualcross correlations. Two conditions must be satisfied for this to occur.First, the multi-user CDMA signal set must have low cross-correlationsfor all possible delays between different user data streams. Second, thepower of the received signals must be similar. If either of theseconditions is not fulfilled, then bit-error-rate and anti-jammingcapabilities of CDMA receivers for multiple users may be degraded. Knownsolutions include using power control or designing CDMA signals withsharper cross correlation properties.

These issues with CDMA signal sets are also present, albeit modified, insituations where legacy (i.e., non-spread) signals are present. Forexample, suppose a system includes an SDR or cognitive transceiver thatmust sense which signals are present and must decide, among otherthings, i) what legacy receiver systems should be supported, ii) whatsignal types to transmit (CDMA, frequency-shift keying, binaryphase-shift keying, quadrature phase-shift keying, etc.), iii) whatsignals parameters to use (frequency, duration, time slots, etc.), iv)what data rates to support, v) what power levels to use, and/or vi) whatdata latency to support. These decisions will be partially based on thetypes and powers of signals already present. Specifically, in order tocoexist in a competitive spectrum environment, signals to be transmittedmust not substantially interfere with current signals, and must not besubstantially interfered with by current signals.

At least some known methods to solve this non-interference problem havelimited ability to operate at relatively low signal to noise ratios(SNRs), leading to incorrect decisions about the presence of legacysignals and therefore incorrect decisions about the signals to transmit.To overcome this, in certain circumstances, correlation can be performedusing specific knowledge about existing signal preambles to operate atlow SNR levels. However, such methods require substantial foreknowledge,which is not likely to be available, and only applies to digitalsignals.

BRIEF DESCRIPTION

In one aspect, a signal processing method is provided. The signalprocessing method includes receiving, at a signal processing system, asignal of interest, calculating, using the signal processing system, apower spectral density for the signal of interest, calculating, usingthe signal processing system, a basis vector based on the power spectraldensity shape, performing, using the signal processing system, a linearregression using the basis vector to generate an estimate for at leastone parameter of the signal of interest, and transmitting, based on theat least one generated estimate, a signal that avoids interference withthe signal of interest.

In another aspect, a signal processing system for processing a signal ofinterest transmitted by a signal source is provided. The signalprocessing system includes a receiver configured to receive the signalof interest from the signal source, a memory device, and a processorcommunicatively coupled to said memory device, said processor configuredto calculate a power spectral density shape for the signal of interest,calculate a basis vector based on the power spectral density, perform alinear regression using the basis vector to generate an estimate for atleast one parameter of the signal of interest, and generate, based onthe at least one generated estimate, a signal that avoids interferencewith the signal of interest.

In yet another aspect, a signal processing method is provided. Thesignal processing method includes receiving, at a signal processingsystem, a signal of interest, determining, using the signal processingsystem, a signal to noise ratio (SNR) for the signal of interest,selecting, using the signal processing system, a signal processingtechnique from a plurality of signal processing techniques based atleast in part on the determined SNR, processing, using the signalprocessing system, the signal of interest using the selected signalprocessing technique to generate an estimate for at least one parameterof the signal of interest, and transmitting, based on the at least onegenerated estimate, a signal that avoids interference with the signal ofinterest.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an exemplary signal processing methodology.

FIG. 2 is a block diagram of an exemplary signal processing methodology.

FIG. 3 includes graphs illustrating a power spectral density of CPFSKsignals for various modulation indices.

FIG. 4 includes graphs illustrating errors for various parameterestimates using the proposed methodology and SNR dependent estimationdescribed herein.

FIG. 5 includes graphs illustrating errors for various parameterestimates by contrast with the proposed methodology and SNR dependentestimation described herein.

FIG. 6 includes a graph demonstrating the statistics of performing anSNR error estimate multiple times.

FIG. 7 includes graphs illustrating the power spectral variation forvarious modulation indices for CPFSK.

FIG. 8 is a flow diagram of exemplary logic for an amalgamation signalprocessing method combing the methods disclosed herein with conventionalsignal processing methods.

FIG. 9 includes a graph showing the performance of the algorithmdescribed in FIG. 8.

FIG. 10 is a block diagram of an exemplary signal processing device.

DETAILED DESCRIPTION

The embodiments described herein allow for estimation of parameters(such as frequency, baud rate, deviation, etc.) of existing but unknownsignals that are relatively weak and/or buried in noise. Estimatingthese parameters enables determining what kinds of signals are presentso that wireless communication systems that compete for spectrum spacecan be configured to broadcast signals at a frequency, baud rate,deviation, etc. that is different from the frequency, baud rate,deviation, etc. of existing but unknown signals, in order to avoidinterference. Thus, the systems and methods described herein improve anability to avoid interference with existing signals when transmitting asignal

Accordingly, the systems and methods described herein facilitateidentifying one or more parameters of an existing signal that may nototherwise be discernable. As such, the systems and methods describedherein may be implemented in any number of real-world signal processingapplications (e.g., wireless communication systems, geolocation systems,etc.).

The systems and methods described herein provide improved signaldetection and parameter estimation of signals from legacy systems,especially for weak signals. As used herein, “legacy signals” refer tosignals transmitted under existing, known formats, and “legacy systems”refer to existing, known signal processing systems. The embodimentsdescribed have the following advantages over legacy systems: ability tooperate far below the communications SNR limit, accurate parameterestimates for signals with low SNR, gradual parameter estimation errorincrease as SNR is lowered (leading to better signal detectiontracking), a very general technique applicable to all legacy signaltypes and others that do not use spreading techniques, and providing amethod with complementary characteristics to traditional signaldetection and parameter estimation, leading to a single amalgamatedmethod covering a wide range of conditions. These advantages providemany benefits directly to software-defined radio (SDR) and cognitiveradio applications operating in a competitive spectrum environment.

FIG. 1 is a block diagram of an exemplary signal processing methodology100. Methodology 100 includes a training component 102 and an operationcomponent 104. At a high-level, training component 102 trains a signalprocessing system for use during execution of operation component 104.More specifically, during training component 102, a plurality of randommessages are generated based on various inputs, power spectral densitiesand basis vectors indicating properties of those power spectraldensities are computed for each random message, and parameter fittingcoefficients for use in operation component 104 are calculated from thebasis vectors. During operation component 104, parameters (e.g.,frequency, baud rate, modulation index, etc.) of a signal of interestare estimated using the parameter fitting coefficients generated as aresult of training component 102. By estimating parameters for a signalof interest, a new, different, original, non-interfering signal can begenerated with parameters different from those of the signal ofinterest, thus avoiding interference between the signal of interest andthe original signal. Training component 102 and operation component 104will now be described in more detail.

During training component 102, a representative set of signals isgenerated, each random signal including a plurality of parameters to beestimated by operation component 104 (e.g., frequency, baud rate,modulation index, etc.), as well as additional parameters that will notbe estimated (e.g., data information). The representative set is createdrandomly to represent how real signals would be distributed. In trainingcomponent 102, results of fitting of parameters to a predetermined basisvector (based on a power spectral density (PSD)) are stored in anoperational form, as described herein.

In training component 102, at block 110, a Federal CommunicationsCommission (FCC) input for signals in the competitive spectrum isprovided. This may be provided, for example, by a user controllingoperation of training component. The FCC input specifies possible rangesfor parameters in the randomly generated signals. At blocks 112, 114,and 116, the ranges for each parameter to be estimated are provided(see, e.g., Table 1 below) by the user. At blocks 118, 120, and 122, theparameters are randomly generated, and a random message is generated atblock 124. A SNR range is provided by the user at block 126, and an SNRvalue is randomly generated at block 128. The generated SNR value isstored in a truth matrix at block 130, and is used to add additive whiteGaussian noise to the generated message at block 132.

At block 134, a coarse power spectral density (PSD) for the message iscalculated. The PSD represents the power spectrum of the message acrossdifferent frequency components. At block 136, a basis vector iscomputed. The basis vector is a vector defined by a predetermined set ofstatistical parameters that represent the shape of the PSD. The basisvector is stored in a basis matrix at block 138. This process may beiteratively repeated to generate and store a plurality of basis vectorsfor each of a plurality of generated messages. At block 140, parameterfitting coefficients and standard deviation error are computed from thebasis vectors. These parameter fitting coefficients are used byoperation component 104 to estimate parameters for a signal of interest.

Once the system is trained from training component 102, the system canbe used to process signals in operation component 104. Specifically, aninput signal, also referred to as a signal of interest, is received atblock 142. From the input, SNR is estimated at block 144, a coarse PSDis computed at block 146, and a legacy estimation system estimatesparameters at block 148. At block 150, a basis vector is computed basedon the PSD, and the parameter fitting coefficients computed at block 140are applied to the computed basis vector at block 152. At blocks 154,156, and 158, parameter estimates are generated, and those estimates areamalgamated at block 160. The amalgamated estimates are provided to aSDR/cognitive radio signal decision system at block 162 for furtherprocessing, as described in detail below.

For ease of explanation, and to show detailed performancecharacteristics, an exemplary implementation is described for processinga specific type of signal used in legacy radio systems. Specifically, inthe particular case of continuous phase frequency shift keying (CPFSK)modulated messages, the generic methodology described in FIG. 1 can berepresented specifically for CPFSK as methodology 200, shown in FIG. 2.Specific implementations of more general components shown in FIG. 1 arelabeled with like reference numerals in FIG. 2. In methodology 200,three parameters (baud rate (BR), frequency deviation (F_(d)), andmodulation index (h)) and SNR are estimated for a signal of interest.

The CPFSK signal will now be described in more detail. The complex formof a CPFSK signal, y(t), can be represented as:

${y(t)} = {\sqrt{\frac{2E}{T}}{\exp \left( {{{j\varphi}\left( {t;I} \right)} + \varphi_{0}} \right)}}$

and a carrier-modulated CPFSK signal can be represented as:

${y(t)} = {\sqrt{\frac{2E}{T}}{\cos \left( {{2\pi \; f_{c}t} + {\varphi \left( {t;I} \right)} + \varphi_{0}} \right)}}$

where f_(c) is the carrier frequency, φ₀ is the initial phase, and

φ(t;I)=θ_(n)+2πhI _(n) q(t−nT),

where h is a modulation index defined as:

h=2f_(d)T

with f_(d) being the maximum frequency deviation, T being the bit length(1/T is the baud rate), and

$\theta_{n} = {\pi \; h{\sum\limits_{k = {- \infty}}^{n - 1}I_{k}}}$${q(t)} = \left\{ \begin{matrix}0 & \left( {t < 0} \right) \\{{t/2}T} & \left( {0 \leq t \leq T} \right. \\{1/2} & \left( {t > T} \right)\end{matrix} \right.$

where I_(k) is the k^(th) bit value defined as a ±1 amplitude (in thecase of binary CPFSK).

Correspondingly, FIG. 3 shows the power spectral density for a binaryCPFSK for various modulation indices h. Notably, the shape of the powerspectral density clearly varies as a function of baud rate, BR, andfrequency deviation (i.e., the parameters to be estimated). Note alsothat the frequency axis (x axis) is normalized by the bit length T sothat the pulse spectral density (PSD) shape shown only depends on h,rather than both f_(d) and T as it would if, as in many cases, T is notknown. This shape change is exploited in statistical methodologydescribed herein to estimate parameters from the power spectral density.

The power spectral density shape approach to {BR, F_(d), h} estimationrequires computing a PSD with a window size commensurate with the signalduration (i.e., message lengths) to be estimated. For short messages, asfew as 16 or 32 samples may be used, whereas longer messages can uselonger windows. For short messages, this results in wide frequency binsbut a more accurate spectral shape estimate. To derive the PSD shape,several statistical parameters derived from the PSD are first computed.Then, basis vectors are computed from these statistical parameters, anda least square fit is done to estimate each of the three CPFSKparameters: BR, F_(d), and h. To control the range of a parameterestimator, it is important to set an expected range of the parameters,and to generate long enough messages so that the estimators havereasonably small variance. The following Table 1 contains the rangesassumed for an example simulation of a particular CPFSK implementationto be described (e.g., the ranges used in blocks 118, 120, and 122). Themethods described herein, however, apply generally to any CPFSKmodulation ranges, not just those listed in Table 1.

TABLE 1 Parameter Range data random BR 8000-24615 bps F_(s) 91553 sps h0.65-0.75 F_(d) 3000-8000 message length 2¹⁶ samples spectral estimationwindow 32 modulation binary CPFSK SNR (db) 0, 5, 10, 15, 20, 25, 30, 35,40

In the exemplary implementation, the ten most valuable statisticalparameters are the frequency at which the peak occurs, the peak value inthe lower and upper half of the PSD, the standard deviations of thelower and upper half of the PSD, and the first and second moments of thelower and upper half of the PSD. These ten statistical parameters werecomputed from a power spectral density vector, Pxx, and itscorresponding frequency vector, F, as shown in the following Table 2using Matlab notation for their definition. These parameters constitutethe basic derivation of shape-related parameters associated with the PSDof a signal. Note that these same statistical parameters can be used forother modulation types, not just CPFSK.

TABLE 2 # Statistical Parameter Description 1 1st frequency peakP1_(max) [P1_(max), I1_(max)] = max_(I<N/2)[P_(XX)]/ Σ_(I<N/2) P_(XX) 2P1_(max) location F1_(Fmax) F1_(max) = F(I1_(Fmax)) 3 2nd frequencyP2_(max) (P2_(max), I2_(max)] = max_(I>N/2)[P_(XX)]/ Σ_(I>N/2)P_(XX) 4P2_(max) location F2_(Fmax) F2_(max) = 1 − F(I2_(Fmax)) 5 1st P_(XX)standard deviation s1 = std_(I<N/2)[P_(XX)]/Σ_(I<N/2)P_(XX) 6 2nd P_(XX)standard deviation s2 = std_(I>N/2)[P_(XX)]Σ/_(I>N/2)P_(XX) 7 1st moment1st P_(XX) n₁ = Σ_(I<N/2)[F(I)P_(XX)(I)]/Σ_(I<N/2)P_(XX) 8 1st moment2nd P_(XX) n₂ = Σ_(I>N/2)[(1 − F(I)P_(XX)(I)]/ Σ_(I>N/2)P_(XX)(I) 9 2ndmoment 1st P_(XX) ns₁ = Σ_(I<N/2)[F(I)²P_(XX)(I)]/ Σ_(I<N/2)P_(XX)(I) 102nd moment 2nd P_(XX) ns₂ = Σ_(I>N/2)[(1 − F(I))²P_(XX)(I)]/Σ_(I>N/2)P_(XX)(I)

From these ten statistical parameters, in an exemplary implementation, abasis vector of length 5 is constructed for each of the N generatedCPFSK messages as shown in the following Table 3. Alternatively, thebasis vector may include be composed of any suitable number and type ofstatistical parameters.

TABLE 3 Coefficient Basis Vector 1 P1_(max) + P2_(max) 2 F1_(max) +F2_(max) 3 s1 + s2 4 n1 + n2 5 {square root over (ns1)} + {square rootover (ns2)}

Three linear regressions were computed, one of each of the parametervectors {BR, F_(d), h} using an N×5 matrix M formed from all the 5element row vectors from each generated CPFSK message as given in thefollowing Table 4 (also in Matlab notation). This results in threevectors {a_(BR),b_(h),c_(Fd)}, each with five elements, corresponding toeach of the parameters to be estimated. These vectors correspond to thelinear estimator of each of the three scalar parameters being estimated{

, {tilde over (F)}_(d), {tilde over (h)}} for a particular estimationusing a given set of statistical parameters in the 1×5 matrix {tildeover (M)}, and this is also shown in Table 4 below.

TABLE 4 Linear Regression Estimator Set M = [({right arrow over(P1_(max))} + {right arrow over (P2_(max))}), {right arrow over((F1_(max))} + {right arrow over (F2_(max))}), ({right arrow over(s1)} + {right arrow over (s2)}), ({right arrow over (n1)} + {rightarrow over (n2)}), {square root over ({right arrow over (ns1)})} +{square root over ({right arrow over (ns2)})})] B = {right arrow over(BR)}/Fs; a_(BR) = M\B; {tilde over (B)}{tilde over (R)} = ({tilde over(M)}a_(BR))F_(s) B = h; b_(h) = M\B; {tilde over (h)} = ({tilde over(M)}b_(h)) B = F_(d)/F_(s); c_(F) _(d) = M\B; {tilde over (F)}_(d) =({tilde over (M)}cF_(d))F_(s)

FIG. 4 shows the results when these estimates are performed for each ofthe SNR values given in Table 1 for long messages. Notably, the resultsare quite good across a relatively wide range of SNR values from 0 to 40dB. The key to this excellent performance is that it requires a separateset of coefficients for each SNR value. In other words, a separate setof coefficient vectors {a_(BR,SNR),b_(h,SNR),c_(Fd,SNR)} is estimatedthrough the linear regression for each SNR value and then the proper setis chosen in a particular case.

By contrast, when an attempt is made to do use one set of coefficientvectors {a_(BR),b_(h),c_(Fd)} across an entire range of SNR's, the (muchpoorer) results are shown in FIG. 5 below. Three things are apparentfrom FIG. 5:

-   -   1) The estimation errors are much larger in the 0 db through 40        db range that was shown in FIG. 4.    -   2) At higher SNRs (e.g., beyond 40 dB), these estimates become        much less accurate. This is because for signals below 40 dB, the        noise provides estimation benefits due to the inherent whitening        of the sample space resulting from some noise being present,        which in term helps statistical methods such as PSD shape        estimation. All the estimators get worst at SNR levels above 40        dB.    -   3) In order to use SNR-dependent coefficients in the estimators,        it is desirable to estimate the SNR reasonably well. The fourth        subfigure of FIG. 5 shows the accuracy of estimating SNR. In        addition, FIG. 6 pictorially displays the estimation errors        within 5 dB SNR ranges. As can be seen, the SNR estimator is        quite good for the lower SNRs from 0 dB to 40 dB, precisely        where it is needed.

To do the SNR estimation accurately requires looking at particularportions of the spectrum that are unaffected by the modulationparameters. FIG. 7 shows the power spectrum for three differentmodulation indices h across a range of SNR's from 0 db to 100 db andvariations in f_(d) and T. These various choices of f_(d) and T explainwhy the PSD shape changes, even though h=2f_(d)T remains the same.

Therefore, the estimation method for SNR concentrates on the center ofthe PSD. This portion of the PSD grows uniformly in power directly asthe noise increases and is otherwise not substantially affected by themodulation index, maximum frequency deviation, or bit length. The twocore statistics used to measure the energy and energy squared in thecenter portion are shown in the following Table 5.

TABLE 5 Statistical Parameter Description NP NP_(j, k) = (Σ_(N) ₀ ^(N) ¹P_(XX))/ΣP_(XX) NP₂ NP_(j, k) = (Σ_(N) ₀ ^(N) ¹ P_(XX) ²)/ΣP_(XX) ²

Then a linear regression to find coefficient vector d_(SNR) is done withapproach as shown in the following Table 6, together with the method toestimate SNR for a particular estimation using a given set ofstatistical parameters in the 1×2 matrix M_(SNR). This estimation usesthe reasonable assumption that there is not another overlapping (infrequency) signal next to the CPFSK signal.

TABLE 6 Linear Regression Estimator Set M_(SNR) = [{right arrow over(NP)}, {right arrow over (NP)}₂] B = {right arrow over (SNR)}; d_(SNR) =M_(SNR)\B; {tilde over (S)}Ñ{tilde over (R)} = {tilde over(M_(SNR))}d_(SNR)

The PSD shape method described herein can be compared against threedifferent existing techniques for estimating baud rate. Specifically,the PSD shape method can be compared against i) (TD) a time-baseddemodulation technique for baud rate estimation, ii) (FD) afrequency-based demodulation technique for baud rate estimation, andiii) (TFD) the TD method using a filtered demodulated signal.

The basic comparison is performed by generating CPFSK messages with thefollowing range of values in Table 7, and then adding Gaussian noise toset particular SNRs, and comparing the estimated results to the actualmessages.

TABLE 7 Parameter Range data random BR 8000-2461 bps F_(s) 91553 sps h0.65-0.75 F_(d) 3000-8000 message length 0.008-0.024 sec spectralestimation window 32 modulation binary CPFSK

The known methods for baud rate estimation involve demodulating theCPFSK message and either operating in the time domain or the frequencydomain to come up with estimates for baud rate. In the time domain, asearch produces the smallest cluster of lengths between bit changes,which should correspond to a single bit length, thus estimating the baudrate. The results in Table 8 below indicate that at 12 dB SNR, thetime-domain (TD) estimator stops working rather abruptly. Thefrequency-domain (FD) method degrades more gracefully, but is generallyworse than the time-domain (TD) method for high SNR. Thefrequency-domain (FD) method demonstrates substantial dependency on theration of F_(d)/BR values in the signal. Further, the TFD methodperforms worse than the TD method at high SNR, but provides a betterfailure indication at lower SNR levels.

Notably, the estimators can give significantly varying results over themodulation index, leading to relatively large potential errors. This isbecause, on short messages in particular, when the BR is very low, thenumber of transitions is small, causing potentially large errors in theBR estimator. Also, the time-domain method may fail to find a cluster ofbit periods, and consequently declare a BR estimator a failure, notreturning an estimate at all. These failure numbers for BR estimationfor the TD method are shown in the following Table 8.

TABLE 8 SNR #failure/total for TD method 12 91/4608  15 0/4608 20 0/4608100 0/4608

Table 8 also illustrates that there is a knee in the curve when thetime-domain method starts to fail (i.e., when the SNR drops by 3 dB from15 dB to 12 dB, the failure rate increases dramatically). In general,below 12 dB SNR, these known methods tend to fail or have significantlylarger errors, which is typically not a problem in conventionalcommunications, since a certain minimal level of SNR is generallyrequired for correct operation, such as bit detection. Some basicconclusions of the comparison are as follows:

i) The PSD shape method described herein works very well for very lowSNR (<12 dB). At higher SNR values, the errors for the PSD shape methodmay be greater than known methods (as would be expected by a method thatdoesn't look at demodulated bits). Furthermore, the PSD method isrelatively ineffective for high SNR applications, due to the variationin the PSD as a function of data variation, unless very long messagesare used.

ii) The performance of the PSD shape method depends on the ranges ofparameters over which it is applied. Results were improved with smallerranges of BR, F_(d), and h. Also, to perform the regression to find thecoefficients, the ranges are predetermined

iii) The PSD method fails more slowly as the SNR goes down, as it is notsubject to gross errors resulting from picking the wrong cluster orpeak.

iv) The TD method fails at SNR levels of 12 dB and below. However, bydemodulating and filtering first before finding zero crossing points,the TFD method can be used as a more reliable failure indicator at lowerSNRs.

After analyzing the strengths and weaknesses of conventional methodsagainst the exemplary PSD shape method, an amalgamation of these fourmethods may be constructed. FIG. 8 is a flow diagram of an exemplarylogic 800 for an amalgamation approach. Logic 800 applies to baud rateestimation, but could be implemented for other parameter types as well.

Logic 800 was used to produce graph 900 shown in FIG. 9. In graph 900,the line shows the RMS error after removing outliers (a much betterrepresentation of true error in most cases). The curve shape representsa nearly optimal approach that captures both ends of the SNR range,which is not possible using only a single estimation method.

In logic 800, at block 802, it is determined whether or not the SNR ofthe input CPFSK signal is less than 12 dB. If the SNR is less than 12dB, flow proceeds to block 804. If the SNR is not less than 12 dB, flowproceeds to block 806. At block 806, the TD method is applied; if the TDmethod fails, flow proceeds to block 808, where the baud rate isestimated using the FD method. If the TD method does not fail, the baudrate is estimated using the TD method at block 810.

Returning to block 804, the TFD method is applied; if the TFD methodfails, flow proceeds to block 812. At block 812, if the differencebetween the results of the TFD method and the FD method is not less thanthe error, flow proceeds to block 814, wherein the baud rate isestimated using the PSD shape method described herein. If the differencebetween the results of the TFD method and the FD method is less than theerror, flow proceeds to block 816, wherein the baud rate is estimatedusing the FD method.

Returning to block 804, if the TFD method does not fail, flow proceedsto block 818. At block 818, if the difference between the results of thePSD shape method and the FD method is not less than the error, flowproceeds to block 820, wherein the baud rate is estimated using the PSDshape method. If the difference between the results of the PSD shapemethod and the FD method is less than the error, flow proceeds to block822, wherein the baud rate is estimated using the FD method.

FIG. 10 is a block diagram of signal processing device 1000 that may beused with methodology 100 (shown in FIG. 1), methodology 200 (Shown inFIG. 2), and logic 800 (shown in FIG. 8). Signal processing device 1000includes at least one memory device 1210 and a processor 1215 that iscoupled to memory device 1210 for executing instructions. In someimplementations, executable instructions are stored in memory device1210. In the exemplary implementation, signal processing device 1000performs one or more operations described herein by programmingprocessor 1215. For example, processor 1215 may be programmed byencoding an operation as one or more executable instructions and byproviding the executable instructions in memory device 1210.

Processor 1215 may include one or more processing units (e.g., in amulti-core configuration). Further, processor 1215 may be implementedusing one or more heterogeneous processor systems in which a mainprocessor is present with secondary processors on a single chip. Inanother illustrative example, processor 1215 may be a symmetricmulti-processor system containing multiple processors of the same type.Further, processor 1215 may be implemented using any suitableprogrammable circuit including one or more systems and microcontrollers,microprocessors, reduced instruction set circuits (RISC), applicationspecific integrated circuits (ASIC), programmable logic circuits, fieldprogrammable gate arrays (FPGA), and any other circuit capable ofexecuting the functions described herein. In the exemplaryimplementation, processor 1215 processes signals to output parameterestimates, as described herein.

In the exemplary implementation, memory device 1210 is one or moredevices that enable information such as executable instructions and/orother data to be stored and retrieved. Memory device 1210 may includeone or more computer readable media, such as, without limitation,dynamic random access memory (DRAM), static random access memory (SRAM),a solid state disk, and/or a hard disk. Memory device 1210 may beconfigured to store, without limitation, application source code,application object code, source code portions of interest, object codeportions of interest, configuration data, execution events and/or anyother type of data. Further, reference templates may be stored on memorydevice 1210.

In the exemplary implementation, signal processing device 1000 includesa presentation interface 1220 that is coupled to processor 1215.Presentation interface 1220 presents information to a user 1225. Forexample, presentation interface 1220 may include a display adapter (notshown) that may be coupled to a display device, such as a cathode raytube (CRT), a liquid crystal display (LCD), an organic LED (OLED)display, and/or an “electronic ink” display. In some implementations,presentation interface 1220 includes one or more display devices.Presentation information 1220 may display, for example, the estimatedsignal parameters.

In the exemplary implementation, signal processing device 1000 includesa user input interface 1235. User input interface 1235 is coupled toprocessor 1215 and receives input from user 1225. User input interface1235 may include, for example, a keyboard, a pointing device, a mouse, astylus, a touch sensitive panel (e.g., a touch pad or a touch screen), agyroscope, an accelerometer, a position detector, and/or an audio userinput interface. A single component, such as a touch screen, mayfunction as both a display device of presentation interface 1220 anduser input interface 1235.

Signal processing device 1000, in the exemplary implementation, includesa communication interface 1240 coupled to processor 1215. Communicationinterface 1240 communicates with one or more remote devices. Tocommunicate with remote devices, communication interface 1240 mayinclude, for example, a wired network adapter, a wireless networkadapter, and/or a mobile telecommunications adapter.

The systems and methods described herein use statistical methods basedon the shape of a signal's power spectral density to pull out signalinformation for use in detection within competitive channels for SDR andcognitive radio applications. The embodiments described herein allow formore precise signal detection and parameter estimation, particularly forweak signals.

Once parameters are estimated for an existing signal of interest, one ormore original signals may be generated and transmitted (e.g., by signalprocessing device 100) such that the one or more original signals avoidinterference with the signal of interest. That is, by generating andtransmitting an original, non-interfering signal having parameter valuesdifferent from those of the estimated parameters of the signal ofinterest, interference between the original signal and the signal ofinterest is reduced.

Further, the embodiments described have the following advantages:ability to operate far below the communications SNR limit, accurateparameter estimates for signals with low SNR, gradual parameterestimation error increase as SNR is lowered (leading to better signaldetection tracking), a very general technique applicable to all legacysignal types including those not CDMA-related, and providing a methodwith complementary characteristics to traditional signal detection andparameter estimation, leading to a single amalgamated method covering awide range of conditions. These advantages provide many benefitsdirectly to SDR and cognitive radio applications operating in acompetitive spectrum environment.

This written description uses examples to disclose variousimplementations, which include the best mode, to enable any personskilled in the art to practice those implementations, including makingand using any devices or systems and performing any incorporatedmethods. The patentable scope is defined by the claims, and may includeother examples that occur to those skilled in the art. Such otherexamples are intended to be within the scope of the claims if they havestructural elements that do not differ from the literal language of theclaims, or if they include equivalent structural elements withinsubstantial differences from the literal language of the claims.

What is claimed is:
 1. A signal processing method comprising: receiving,at a signal processing system, a signal of interest; calculating, usingthe signal processing system, a power spectral density for the signal ofinterest; calculating, using the signal processing system, a basisvector based on the power spectral density shape; performing, using thesignal processing system, a linear regression using the basis vector togenerate an estimate for at least one parameter of the signal ofinterest; and transmitting, based on the at least one generatedestimate, a signal that avoids interference with the signal of interest.2. A signal processing method in accordance with claim 1, whereinreceiving a signal of interest comprises receiving a signal of interestat a software-defined radio system.
 3. A signal processing method inaccordance with claim 1, wherein performing a linear regressioncomprises performing a linear regression to generate an estimate for afrequency deviation of the signal of interest.
 4. A signal processingmethod in accordance with claim 1, wherein performing a linearregression comprises performing a linear regression to generate anestimate for a baud rate of the signal of interest.
 5. A signalprocessing method in accordance with claim 1, wherein performing alinear regression comprises performing a linear regression to generatean estimate for a modulation index of the signal of interest.
 6. Asignal processing method in accordance with claim 1, wherein receiving asignal of interest comprises receiving a signal of interest having asignal to noise ratio less than 12 dB.
 7. A signal processing method inaccordance with claim 1, wherein receiving a signal of interestcomprises receiving a continuous phase frequency shift keying (CPFSK)modulated message.
 8. A signal processing system for processing a signalof interest transmitted by a signal source, said signal processingsystem comprising: a receiver configured to receive the signal ofinterest from the signal source; a memory device; and a processorcommunicatively coupled to said memory device, said processor configuredto: calculate a power spectral density shape for the signal of interest;calculate a basis vector based on the power spectral density; perform alinear regression using the basis vector to generate an estimate for atleast one parameter of the signal of interest; and generate, based onthe at least one generated estimate, a signal that avoids interferencewith the signal of interest.
 9. A signal processing system in accordancewith claim 8, wherein said signal processing system is asoftware-defined radio system.
 10. A signal processing system inaccordance with claim 8, wherein to perform a linear regression, saidprocessor is configured to perform a linear regression to generate anestimate for a frequency deviation of the signal of interest.
 11. Asignal processing system in accordance with claim 8, wherein to performa linear regression, said processor is configured to perform a linearregression to generate an estimate for a baud rate of the signal ofinterest.
 12. A signal processing system in accordance with claim 8,wherein to perform a linear regression, said processor is configured toperform a linear regression to generate an estimate for a modulationindex of the signal of interest.
 13. A signal processing system inaccordance with claim 8, wherein to receive a signal of interest, saidreceiver is configured to receive a signal of interest having a signalto noise ratio less than 12 dB.
 14. A signal processing system inaccordance with claim 8, wherein to receive a signal of interest, saidreceiver is configured to receive a continuous phase frequency shiftkeying (CPFSK) modulated message.
 15. A signal processing methodcomprising: receiving, at a signal processing system, a signal ofinterest; determining, using the signal processing system, a signal tonoise ratio (SNR) for the signal of interest; selecting, using thesignal processing system, a signal processing technique from a pluralityof signal processing techniques based at least in part on the determinedSNR; processing, using the signal processing system, the signal ofinterest using the selected signal processing technique to generate anestimate for at least one parameter of the signal of interest; andtransmitting, based on the at least one generated estimate, a signalthat avoids interference with the signal of interest.
 16. A signalprocessing method in accordance with claim 15, wherein selecting asignal processing technique comprises selecting a signal processingtechnique based on whether or not the determined SNR is below 12 dB. 17.A signal processing method in accordance with claim 15, wherein theplurality of signal processing techniques include a time-baseddemodulation technique, a frequency-based demodulation technique, afiltered time-based demodulation technique, and a power spectral densitytechnique.
 18. A signal processing method in accordance with claim 15,wherein receiving a signal of interest comprises receiving a signal ofinterest at a software-defined radio system.
 19. A signal processingmethod in accordance with claim 15, wherein receiving a signal ofinterest comprises receiving a continuous phase frequency shift keying(CPFSK) modulated message.
 20. A signal processing method in accordancewith claim 15, wherein processing the signal of interest comprisesprocessing the signal of interest to generate an estimate for at leastone of a frequency deviation, a baud rate, and a modulation index of thesignal of interest.